Nicholas N. Bennett

Fast Model Updates Using Wavelets

Solving an inverse problem means determining the parameters of a model given a set of measurements. In solving many practical inverse problems, accounting for the uncertainty of the solution is very important in aiding decision-making. A standard approach to do this begins by choosing a model parametrization and then using a Bayesian approach to make inferences on the model parameters from measurement data. However, this quantified uncertainty is a function of the model parametrization and for many inverse problems; there are many model parametrizations that account for the data equally well. A well-known approach to accounting for model uncertainty is Bayesian model averaging, where many model parametrizations are considered. Significant computational costs are associated with this method because one must compute the posterior distribution for each model parametrization.We consider a family of model parametrizations given by decimated wavelet bases. By decimated wavelet basis we mean a subset of the mode...